The method for calculating the support reactions of a statically indeterminable final drive shaft of a tractor drive axle

BACKGROUND: Currently, in the design of vehicle drive axles, bevel final drives are used, forming both statically determinable structures and statically indeterminable ones. In the first case, the bearings, on which the bevel final drive shafts rest, form two rows of rolling elements, in the second case — three or more. Despite the prevalence of bevel final drive designs that form statically indeterminable structures, the statically determinable structures are considered in the process of teaching the design and calculation of machine elements. The study relevance lies in the formalization of the analytical calculation of the reactions on the supports of the bevel final drive, forming a statically indeterminable system, with the derivation of formulae for determining the reactions in the extra support.

AIM: Formalization of the method for calculating the support reactions of the drive axle bevel final drive as a statically indeterminable system, used for analysis of bearings.

METHODS: The study is based on mathematical dependencies of Analytical Mechanics to calculate reactions in the main supports, a corollary of Castigliano theorem and the force method to calculate reactions in extra supports. The Mathcad software was used for mathematical calculations.

RESULTS: A formalized method for the analytical analysis of support reactions in statically indeterminable systems, using Castigliano theorem to solve static indetermination, has been developed and presented. The application of the method for calculating the support reactions of the statically indeterminable driveshaft of the bevel final drive of the drive axle of the Kirovets K-7 series tractors is considered.

CONCLUSION: The dependencies obtained during the calculations make it possible to calculate the support reactions of the bevel final drive, the design of which forms a statically indeterminable system. The mathematical model of the bevel final drive, obtained during the calculations, can be used as a basis for developing software that automates this analysis.